34
about the others. In contrast to the time domain, the space domain is
bounded in all three dimensions. The longitude domain is periodic, which
enables it to be represented by Fourier harmonics (zonal wave numbers
0, 1, 2 .. ). Latitudinal variability can be represented in terms of Legendre
polynomials. Global or hemispheric patterns on a horizontal surface can be
represented in terms of spherical harmonics which are products of sine and
cosine functions in longitude and Legendre polynomials in latitude (e.g.,
see Washington and Parkinson 1986). Just as power spectra can be used
to describe and categorize temporal variability, one dimensional spectra on
latitude circles or two dimensional spectra based on spherical harmonics
can be used to describe and categorize spatial variability. Fourier decomposition of wind and pressure patterns on latitude circles is implicit in many
theoretical treatments of baroclinic waves, stratospheric planetary waves,
and equatorially trapped waves. The disturbances are represented in terms
of sinusoidal variations in longitude modulated by a latitude- height profile
of amplitude and phase. Observations are often analyzed in terms of the
same conceptual framework.
If a continuous field defined on a spherical surface were characterized
by isotropic red noise, where 'red', in this context, refers to the space
domain, the EOF's would assume the form of spherical harmonics (North,
1975). In analogy with the red noise time series considered in section
2.3 of chapter 1, the degree of separation between successive eigenvalues
would be determined by the degree of redness in the space domain (i.e.,
the strength of the temporal autocorrelation between the fluctuations at
adjacent gridpoints). In the absence of longitudinal asymmetries in the
bottom boundary conditions, the circulation would be dominated by such
structures. The leading EOF's ofthe wintertime 50-mb height field (located
in the lower stratosphere at an altitude near 20 km), exhibit the kind of
geometrical symmetry that is characteristic of spherical harmonics (Fig.
1).
2.3 Considerations of data availability
The types of analyses that can be performed to investigate the structure
and evolution of climate variability are constrained by the availability of
suitable data sets. In general, the longer the temporal scope of the investigation, the more limited the spatial sampling and the greater the concerns
about the homogeneity of the record in the time domain. This section
about the others. In contrast to the time domain, the space domain is
bounded in all three dimensions. The longitude domain is periodic, which
enables it to be represented by Fourier harmonics (zonal wave numbers
0, 1, 2 .. ). Latitudinal variability can be represented in terms of Legendre
polynomials. Global or hemispheric patterns on a horizontal surface can be
represented in terms of spherical harmonics which are products of sine and
cosine functions in longitude and Legendre polynomials in latitude (e.g.,
see Washington and Parkinson 1986). Just as power spectra can be used
to describe and categorize temporal variability, one dimensional spectra on
latitude circles or two dimensional spectra based on spherical harmonics
can be used to describe and categorize spatial variability. Fourier decomposition of wind and pressure patterns on latitude circles is implicit in many
theoretical treatments of baroclinic waves, stratospheric planetary waves,
and equatorially trapped waves. The disturbances are represented in terms
of sinusoidal variations in longitude modulated by a latitude- height profile
of amplitude and phase. Observations are often analyzed in terms of the
same conceptual framework.
If a continuous field defined on a spherical surface were characterized
by isotropic red noise, where 'red', in this context, refers to the space
domain, the EOF's would assume the form of spherical harmonics (North,
1975). In analogy with the red noise time series considered in section
2.3 of chapter 1, the degree of separation between successive eigenvalues
would be determined by the degree of redness in the space domain (i.e.,
the strength of the temporal autocorrelation between the fluctuations at
adjacent gridpoints). In the absence of longitudinal asymmetries in the
bottom boundary conditions, the circulation would be dominated by such
structures. The leading EOF's ofthe wintertime 50-mb height field (located
in the lower stratosphere at an altitude near 20 km), exhibit the kind of
geometrical symmetry that is characteristic of spherical harmonics (Fig.
1).
2.3 Considerations of data availability
The types of analyses that can be performed to investigate the structure
and evolution of climate variability are constrained by the availability of
suitable data sets. In general, the longer the temporal scope of the investigation, the more limited the spatial sampling and the greater the concerns
about the homogeneity of the record in the time domain. This section